As Kayne (1994) has shown, the theory of antisymmetry of syntax also provides an explanation of a structural property of morphological complexes, the Righthand Head Rule. In this paper we show that an antisymmetry approach to the Righthand Head Rule eventually is to be preferred on empirical grounds, because it describes and explains the properties of a set of hitherto puzzling morphological processes -known as discontinuous affixation, circumfixation or parasyn-thesis. In considering these and a number of more standard morphological structures, we argue that one difference bearing on the proper balance between morphology and syntax should be re-installed (re- with respect to Kayne), a difference between the antisymmetry of the syntax of morphology and the antisymmetry of the syntax of syntax proper.